Noncompact Heisenberg spin magnets from high-energy QCD: II. Quantization conditions and energy spectrum

TL;DR

This paper analyzes the spectrum of compound reggeized gluon states in high-energy QCD using a noncompact Heisenberg spin magnet model, employing Baxter Q-operator methods to derive quantization conditions and energy spectra.

Contribution

It provides a complete spectrum description of reggeized gluon states in QCD via a novel application of the Baxter Q-operator to a noncompact SL(2,C) spin magnet.

Findings

Interception of states with even N exceeds one, odd N is less than one.

Interception values approach one as N becomes large.

Explicit eigenvalues of the Q-operator are obtained.

Abstract

We present a complete description of the spectrum of compound states of reggeized gluons in QCD in multi-colour limit. The analysis is based on the identification of these states as ground states of noncompact Heisenberg SL(2,C) spin magnet. A unique feature of the magnet, leading to many unusual properties of its spectrum, is that the quantum space is infinite-dimensional and conventional methods, like the Algebraic Bethe Ansatz, are not applicable. Our solution relies on the method of the Baxter Q-operator. Solving the Baxter equations, we obtained the explicit expressions for the eigenvalues of the Q-operator. They allowed us to establish the quantization conditions for the integrals of motion and, finally, reconstruct the spectrum of the model. We found that intercept of the states built from even (odd) number of reggeized gluons, N, is bigger (smaller) than one and it decreases (increases) with N approaching the same unit value for infinitely large N.